If you purchase a RETAIL version of a Microsoft OS you generally have rights to TRANSFER that license to another machine. That and getting support directly from Microsoft are really the major differences between an OEM and a retail license (and $100 or so).

So, if that box was from Dell, HP, etc, it probably has an OEM license and Microsoft could (but likely would not) deny you an activation. If that was a homebuilt PC and the builder bought a retail version of the OS from a store you are within you rights to move that license and get a activation code.

Either way, its unlikely you would be denied an activation code unless you have installed that same license many times.